Hey Philo
Welcome! I know the hopelessness you're feeling. You're not alone.
When I'm deep in my addiction, and life has become completely unmanageable, I can get very overwhelmed. The only way for me to untie the knots my life is in is to take it one step, one problem, at a time. Don't look at the whole knotted mess, just one part of the knot. There is absolutely no way to start however without getting sober. So that's priority 1. All the other stuff will be there, so just focus on not drinking. AA is a great way to meet other people in your shoes. Or there's Smart Recovery. I would highly recommend some F2F support. Even if the meetings are foreign to you, or don't seem a perfect fit, just being with people like you will help a lot.
Mental illness. Got it. Alcohol makes bipolar symptoms far worse. And lithium and alcohol? Well, I think you know.
Weight gain. Its your whole lifestyle. Lithium does cause weight gain. But combine it with booze, poor diet, and no exercise? Voila.
One step at a time, one day at a time. Ask your dr about medically assisted detox to help you through. I'm glad you're getting blood work. You can do this!